In the \({\cal N}=4\)  case, the super-Cotton tensor is a primary scalar
superfield \({\cal W}\)  of dimension 1
constrained by [1]}
\(\nabla ^{\alpha I}\nabla _{\alpha }^J {\cal W}=\frac{1}{4}\delta ^{IJ}\nabla ^{\alpha K}\nabla _{\alpha }^K {\cal W}~.\) 
